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The Beta‐Pochhammer and its application to arbitrary threshold phase error probability of a vector in Gaussian noise.
- Source :
-
Mathematical Methods in the Applied Sciences . Sep2023, Vol. 46 Issue 13, p14547-14575. 29p. - Publication Year :
- 2023
-
Abstract
- This paper develops a calculus around a new β‐Pochhammer symbol of two variables, (a,b)m,n based on the Beta weighting ta−11−tb−1. The approach is a natural rising factorial formulation that offers a new way to express hypergeometric functions of two variables. The results are implemented to solve the problem of finding the phase error probability of a vector perturbed by Gaussian noise with an arbitrary phase threshold in closed form for the first time, in terms of the incomplete confluent hypergeometric function 1ℱ1. This has been an unresolved problem in angle modulation dating back to the 1950s. Closed‐form solutions are developed around the lower and upper incomplete Humbert second Φ2 confluent hypergeometric function of two variables using the new incomplete β‐Pochhammer calculus. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01704214
- Volume :
- 46
- Issue :
- 13
- Database :
- Academic Search Index
- Journal :
- Mathematical Methods in the Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 169971118
- Full Text :
- https://doi.org/10.1002/mma.9335